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摘要:
针对多节点InSAR机翼挠曲变形误差问题，提出了一种基于机理模型综合参数辨识的方法对空气扰动影响机翼挠曲变形分层建模。首先，将大气湍流作为InSAR成像工作段的主要空气扰动，并基于Dryden模型分析得出了载机工作高度和速度是影响大气湍流的主要因素，将大气湍流影响机翼挠曲变形建模转换为载机在不同工作状态（高度变化、速度变化）的机翼挠曲变形分层建模。其次，基于空气动力学理论及悬臂梁变形理论建立机翼挠曲变形机理模型，借助计算流体力学与计算结构力学仿真分析获取实验数据辨识模型参数。最后，通过仿真实验验证，所提方法与模态叠加原理计算横向位移精度均优于0.6 mm（相对误差0.3%），轴向位移精度均优于0.015 mm（相对误差0.2%）。对实验室搭建的分布式光纤光栅测量系统进行测试，利用模态叠加原理计算变形量来验证所提方法，横向位移精度优于0.3 mm（相对误差1%），轴向位移精度优于0.06 mm（相对误差3%）。
Abstract:For the problem of multi-node InSAR wing deflection deformation error, a method based on mechanism modeling integrated parameter identification is proposed for the layered modeling of wing deflection deformation induced by air disturbance. First, this model takes atmospheric turbulence as the main air disturbance in the InSAR imaging working section, and based on Dryden model, it is analyzed that the working height and speed of the aircraft are the main factors affecting atmospheric turbulence. Therefore, the modeling of wing deformation affected by atmospheric turbulence is transformed to the layered modeling of wing deformation under different working conditions (height change, velocity change). Second, the wing deformation mechanism model is established based on the combination of the aerodynamic theory and the cantilever beam deformation theory. The parameters of the model are identified by the experimental data obtained from the simulation analysis of computational fluid dynamics and computational structural mechanics. Finally, the simulation experiments show that, calculated by both the proposed method and the mature modal superposition principle, the lateral displacement error is better than 0.6 mm (relative error 0.3%) and the axial displacement error is better than 0.015 mm (relative error 0.2%). In addition, based on the distributed fiber Bragg grating measurement system of wing structure built in the laboratory and the principle of modal superposition, the deformation is calculated to verify the proposed method, the lateral displacement error is better than 0.3 mm (relative error 1%) and the axial relative error is better than 0.06 mm (relative error 3%).
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图 6 机翼所受气动载荷及湍流速度变化
Figure 6. Changes in aerodynamic loads and turbulent velocity on wing
图 9 不同工况下测点15的机翼挠曲变形
Figure 9. Wing deflection deformation at measuring point 15 under different conditions
表 1 铝合金7075材料属性
Table 1. Aluminum alloy 7075 material properties
参数 数值 密度/(g·cm-3) 2.81 极限抗拉强度/MPa 524 极限屈服强度/MPa 455 弹性模量/GPa 71 泊松比 0.33 
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工作高度/km 压力/Pa 温度 密度/(g·cm-3) 摄氏度 开尔文 2.0 79 810 2.35 275.5 1.009 3.0 70 510 -3.25 269.9 0.908 7 3.5 66 100 -6.27 266.88 0.862 5 4.0 61 950 -9.29 263.86 0.818 1 4.5 58 070 -12.3 260.85 0.775 6 5.0 54 420 -15.32 257.83 0.734 8 5.5 51 000 -18.34 254.81 0.695 6 6.0 47 680 -21.62 251.53 0.658 9 6.5 44 520 -24.97 248.18 0.623 7 7.0 41 580 -28.32 244.83 0.59 7.5 38 770 -31.65 241.5 0.557 7 8.0 36 080 -35.07 238.08 0.526 8
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表 3 载机工作速度影响的参数辨识结果
Table 3. Parameter identification results of carrier speed
测点 u=Av2 R2 SSE u=Av2.014 R2 SSE u=Av2.015 R2 SSE 2 u=6.492×10-7v2 1.000 7.22×10-10 u=6.022×10-8v2.014 1.000 1.33×10-11 u=5.99×10-8v2.015 1.000 4.57×10-12 7 u=1.001×10-6v2 1.000 1.57×10-7 u=9.284×10-7v2.014 1.000 1.52×10-9 u=9.234×10-7v2.015 1.000 3.34×10-11 12 u=2.407×10-6v2 1.000 8.96×10-7 u=2.233×10-6v2.014 1.000 7.67×10-9 u=2.221×10-6v2.015 1.000 1.74×10-9 15 u=3.424×10-6v2 1.000 1.82×10-6 u=3.176×10-6v2.014 1.000 1.52×10-8 u=3.159×10-6v2.015 1.000 2.98×10-9
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表 4 载机工作高度影响的参数辨识结果
Table 4. Parameter identification results of carrier's working height
测点 指数函数u=aebP R2 SSE 线性模型u=aP+b R2 SSE 幂函数u=aP0.833 R2 SSE 2 u=2.286×10-8e1.368×10-5P 0.996 1.42×10-18 u=7.27P×10-13+8.696×10-9 1.000 5.08×10-20 u=5.484×10-12P0.833 1.000 8.60×10-21 7 u=3.522×10-7e1.368×10-5P 0.996 3.52×10-16 u=1.121P×10-11+1.339×10-7 1.000 1.51×10-17 u=8.454×10-11P0.833 1.000 2.82×10-18 12 u=8.467×10-7e1.369×10-5P 0.996 2.05×10-15 u=2.696P×10-11+3.215×10-7 1.000 9.16×10-17 u=2.033×10-10P0.833 1.000 1.80×10-17 15 u=1.205×10-6e1.368×10-5P 0.996 4.16×10-15 u=3.834P×10-11+4.585×10-7 1.000 1.89×10-16 u=2.892×10-10P0.833 1.000 3.74×10-17
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表 5 本文模型预测Y向变形
Table 5. Y-direction deformation predicted by proposed model
工作速度/(m·s-1) 工作高度/km ANSYS Workbench
Y向变形量/mm本文模型
Y向变形量/mm测点7 测点12 测点15 测点7 测点12 测点15 250 1.5 3.85 4.38 4.30 3.85 4.37 4.31 200 1.5 2.45 2.79 2.74 2.46 2.79 2.75 2.0 2.33 2.65 2.60 2.33 2.65 2.61 6.5 1.44 1.63 1.61 1.43 1.63 1.61 7.0 1.36 1.54 1.52 1.35 1.54 1.52 7.5 1.28 1.46 1.44 1.28 1.45 1.43 8.0 1.21 1.38 1.36 1.20 1.37 1.35 185 2.5 1.89 2.15 2.12 1.89 2.15 2.12 235 2.5 3.07 3.48 3.44 3.06 3.48 3.44 285 2.5 4.52 5.14 5.07 4.52 5.14 5.07
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表 6 本文模型预测Z向变形
Table 6. Z-direction deformation predicted by proposed model
工作速度/(m·s-1) 工作高度/km ANSYS Workbench
Z向变形量/mm本文模型
Z向变形量/mm测点7 测点12 测点15 测点7 测点12 测点15 250 1.5 73.36 176.36 250.83 73.24 176.14 250.56 200 1.5 46.80 112.48 159.97 46.72 112.35 159.82 2.0 44.44 106.81 151.91 44.37 106.69 151.77 6.5 27.31 65.67 93.41 27.28 65.61 93.33 7.0 25.81 62.08 88.31 25.77 61.98 88.17 7.5 24.38 58.64 83.43 24.31 58.47 83.17 8.0 23.01 55.35 78.75 22.90 55.07 78.34 185 2.5 36.04 86.66 123.28 36.01 86.60 123.19 235 2.5 58.36 140.34 199.63 58.32 140.24 199.49 285 2.5 86.05 206.92 294.36 86.02 206.86 294.26
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表 7 Y向变形模态叠加原理计算结果
Table 7. Y-direction deformation calculated by modal superposition principle
工作速度/(m·s-1) 工作高度/km ANSYS Workbench
Y向变形量/mm模态叠加原理
Y向变形量/mm测点7 测点12 测点15 测点7 测点12 测点15 250 1.5 3.85 4.38 4.30 3.85 4.37 4.30 200 1.5 2.45 2.79 2.74 2.45 2.79 2.74 2.0 2.33 2.65 2.60 2.33 2.65 2.60 6.5 1.44 1.63 1.61 1.44 1.63 1.61 7.0 1.36 1.54 1.52 1.36 1.54 1.52 7.5 1.28 1.46 1.44 1.28 1.46 1.44 8.0 1.21 1.38 1.36 1.21 1.38 1.36 185 2.5 1.89 2.15 2.12 1.89 2.15 2.12 235 2.5 3.07 3.48 3.44 3.07 3.49 3.43 285 2.5 4.52 5.14 5.07 4.52 5.14 5.06
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表 8 Z向变形模态叠加原理计算结果
Table 8. Z-direction deformation calculated by modal superposition principle
工作速度/(m·s-1) 工作高度/km ANSYS Workbench
Z向变形量/mm模态叠加原理
Z向变形量/mm测点7 测点12 测点15 测点7 测点12 测点15 250 1.5 73.36 176.36 250.83 73.24 176.03 250.31 200 1.5 46.80 112.48 159.97 46.70 112.23 159.54 2.0 44.44 106.81 151.91 44.35 106.58 151.52 6.5 27.31 65.67 93.41 27.28 65.60 93.31 7.0 25.81 62.08 88.31 25.80 62.02 88.24 7.5 24.38 58.64 83.43 24.37 58.60 83.37 8.0 23.01 55.35 78.75 23.01 55.32 78.72 185 2.5 36.04 86.66 123.28 36.00 86.56 123.13 235 2.5 58.36 140.34 199.63 58.31 140.18 199.40 285 2.5 86.05 206.92 294.36 85.97 206.70 294.02
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表 9 本文模型与模态叠加原理计算误差值对比
Table 9. Comparison of error values calculated by proposed model and modal superposition principle
工作速度/(m·s-1) 工作高度/km Y向 Z向 ANSYS仿真位移/mm 模态叠加原理误差/mm 本文模型误差/mm ANSYS仿真位移/mm 模态叠加原理误差/mm 本文模型误差/mm 250 1.5 4.30 0.004 0.011 250.83 0.520 0.303 200 1.5 2.74 0.004 0.013 159.97 0.426 0.182 2.0 2.60 0.004 0.011 151.91 0.388 0.169 6.5 1.61 0.002 0.002 93.41 0.101 0.084 7.0 1.52 0.002 0.004 88.31 0.078 0.146 7.5 1.44 0.002 0.007 83.43 0.054 0.251 8.0 1.36 0.002 0.010 78.75 0.031 0.415 185 2.5 2.12 0.002 0.002 123.28 0.155 0.091 235 2.5 3.44 0.003 0.003 199.63 0.232 0.148 285 2.5 5.07 0.004 0.003 294.36 0.341 0.109
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表 10 全站仪测量值
Table 10. Total station measurement values
加载/N Y向位移/mm Z向位移/mm 测点1 测点2 测点1 测点2 4.9 -0.18 -0.18 -2.97 -4.50 9.8 -0.34 -0.42 -5.70 -8.70 14.7 -0.56 -0.57 -8.51 -13.01 19.6 -0.79 -0.84 -11.45 -17.49 24.5 -0.96 -1.06 -14.17 -21.66 29.4 -1.14 -1.32 -16.95 -25.93 34.3 -1.36 -1.55 -19.66 -29.98 39.2 -1.57 -1.81 -22.45 -34.24 44.1 -1.77 -2.04 -25.13 -38.30 49 -2.06 -2.28 -27.88 -42.32
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表 11 预测值与全站仪测量值对比
Table 11. Comparison of predicted and total station measurement values
测点 加载/N Y向位移/mm Z向位移/mm 全站仪测量值 本文方法预测值 绝对误差 全站仪测量值 本文方法预测值 绝对误差 测点1 39.2 -1.57 -1.51 0.06 -22.45 -22.52 0.07 44.1 -1.77 -1.78 0.01 -25.13 -25.08 0.05 49 -2.06 -2.06 0 -27.88 -27.57 0.31 测点2 39.2 -1.81 -1.84 0.03 -34.24 -34.41 0.17 44.1 -2.04 -2.09 0.05 -38.3 -38.39 0.09 49 -2.28 -2.34 0.06 -42.32 -42.31 0.01
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